Steady-state Displacement Research Articles

Numerical and experimental study on silicon microresonators based on phononic crystal slabs with reduced central-hole radii

In this paper, we report the numerical and experimental study on micromechanical resonators which are made by introducing defects on an otherwise perfect two-dimensional (2D) silicon phononic crystal (PnC) slab. The 2D PnC slab is made by etching a square array of cylindrical air holes in a free-standing silicon plate with a thickness of 10 µm, while the defects are created by reducing the radii of three rows of air holes at the centre of the 2D PnC slab. Three resonators with different values of reduced radii, i.e., 2 µm, 4 µm and 6 µm, are included in this study. The finite-element-modelling method is used to calculate the band structure of the perfect 2D PnC slab and to analyse the different mode shapes of the structure. The design, numerical modelling, fabrication process, as well as characterization results and discussions of the three PnC resonators are also included. Due to its CMOS-compatibility, aluminium nitride is chosen to be the piezoelectric material of the inter-digital transducers, which are used to generate and detect acoustic waves. Testing is done to characterize the resonant frequency (f), quality factor (Q), as well as insertion loss of each of the three microfabricated PnC resonators and the results are discussed by analysing the simulated transmission spectra, the defected band structures, and the steady-state displacement profiles of the structures at their respective resonant frequencies. The experimental results show that the designed PnC resonators with reduced central-hole radii have higher resonant frequency and higher quality factors as compared to their normal Fabry–Perot counterpart, thanks to the higher-frequency modes supported within the cavity and slow sound effect in the lateral direction introduced by the central holes with reduced radii, respectively. As a result, the achieved (f-Q) product can be as high as 2.96 × 1011, which is among the highest for silicon resonators operating in air.

Optimization of multiple tuned mass dampers for vibration control of system under external excitation

Using a numerical searching technique the optimum parameters of multiple tuned mass dampers (MTMD) for suppressing the dynamic response of a damped main system subjected to external excitation are investigated. The criteria selected for the optimality is the minimization of the steady-state displacement of the main system under external harmonic excitation. The parameters of the MTMD that are optimized include: the damping ratio, the tuning frequency ratio and the frequency band-width. The optimum parameters of the MTMD system and corresponding steady-state displacement are obtained for different damping ratios of the main system and the mass ratios of the MTMD system. The explicit formulae for the optimum parameters of MTMD (i.e. damping ratio, band-width and tuning frequency) are then derived using a curve-fitting scheme that can readily be used for engineering applications. The error in the proposed explicit expressions is investigated and found to be quite negligible. The effectiveness of optimally designed MTMD system is also compared with that of the optimum single tuned mass damper and it is observed that the optimally designed MTMD system is found to be more effective for vibration control than the single tuned mass damper. Further, the damping in the main system significantly influences the optimum parameters and the effectiveness of the MTMD system. Finally, a sensitivity analysis of optimally designed MTMD system to study its performance under uncertainty in the parameter is also carried out.

高知市付近で１９７７〜１９８０年頃に発生した長期的スロースリップ

We extracted unsteady vertical crustal deformations in the Shikoku region before GPS deployment using leveling and sea-level data. GPS-derived, steady-state vertical displacements related to ongoing subduction of the Philippine Sea plate were subtracted from the vertical displacements observed by leveling surveys. Monthly mean sea-level data were corrected for atmospheric pressure and hydrographic effects. As a result, we found an upheaval of 4-5cm near Kochi City from 1977 to 1980 in both the leveling and sea-level data. This may represent a crustal deformation caused by a long-term slow slip event on the plate boundary.

A Dynamic Network Model for Two-Phase Flow in Porous Media

We present a dynamic model of immiscible two-phase flow in a network representation of a porous medium. The model is based on the governing equations describing two-phase flow in porous media, and can handle both drainage, imbibition, and steady-state displacement. Dynamic wetting layers in corners of the pore space are incorporated, with focus on modeling resistivity measurements on saturated rocks at different capillary numbers. The flow simulations are performed on a realistic network of a sandpack which is perfectly water-wet. Our numerical results show saturation profiles for imbibition in agreement with experiments. For free spontaneous imbibition we find that the imbibition rate follows the Washburn relation, i.e., the water saturation increases proportionally to the square root of time. We also reproduce rate effects in the resistivity index for drainage and imbibition.

Measurement of pulsatile motion with millisecond resolution by MRI

We investigated a technique based on phase-contrast cine MRI combined with deconvolution of the phase shift waveforms to measure rapidly varying pulsatile motion waveforms. The technique does not require steady-state displacement during motion encoding. Simulations and experiments were performed in porcine liver samples in view of a specific application, namely the observation of transient displacements induced by acoustic radiation force. Simulations illustrate the advantages and shortcomings of the methods. For experimental validation, the waveforms were acquired with an ultrafast ultrasound scanner (Supersonic Imagine Aixplorer), and the rates of decay of the waveforms (relaxation time) were compared. With bipolar motion-encoding gradient of 8.4 ms, the method was able to measure displacement waveforms with a temporal resolution of 1 ms over a time course of 40 ms. Reasonable agreement was found between the rate of decay of the waveforms measured in ultrasound (2.8 ms) and in MRI (2.7-3.3 ms).

Two-Dimensional Stresses in a Hollow FG Sphere with Heat Source

This work studied the theoretical solution for axisymmetric steady-state mechanical and thermal stresses in hollow functionally graded spheres with respect to heat source. The material properties of the FG sphere change continuously across the thickness direction according to the power functions of radial direction. The steady-state temperature, displacements, and stresses are derived due to the general mechanical and thermal boundary conditions as function of radial and circumferential directions. The temperature and Navier equations are solved analytically, using Taylor and Legendre series. With increasing the power law indices the temperature distribution due to heat source is decreased. Circumferential stress and radial displacement due to heat source are decreased as the power law index increases.

Effects of gravity on the stability of the steady propagation of a liquid plug in a small conduit

In this work we numerically study the stability of the steady state displacement of a liquid plug in a capillary tube when gravity, inertia and surface forces are important. The methodology employed is based on the analysis of steady state solutions and has been presented in previous publications. Gravity is assumed to act only along the axis of the tube.

One-way mode transmission in one-dimensional phononic crystal plates

We investigate theoretically the band structures of one-dimensional phononic crystal (PC) plates with both antisymmetric and symmetric structures, and show how unidirectional transmission behavior can be obtained for either antisymmetric waves (A modes) or symmetric waves (S modes) by exploiting mode conversion and selection in the linear plate systems. The theoretical approach is illustrated for one PC plate example where unidirectional transmission behavior is obtained in certain frequency bands. Employing harmonic frequency analysis, we numerically demonstrate the one-way mode transmission for the PC plate with finite superlattice by calculating the steady-state displacement fields under A modes source (or S modes source) in forward and backward direction, respectively. The results show that the incident waves from A modes source (or S modes source) are transformed into S modes waves (or A modes waves) after passing through the superlattice in the forward direction and the Lamb wave rejections in the backward direction are striking with a power extinction ratio of more than 1000. The present structure can be easily extended to two-dimensional PC plate and efficiently encourage practical studies of experimental realization which is believed to have much significance for one-way Lamb wave mode transmission.

Design of a Linear Ultrasonic Piezoelectric Motor

A new geometrically unique ultrasonic motor (USM) was designed, prototyped, and tested. USMs operate by vibrating a drive tip in an elliptical motion while in periodic contact with a driven surface. Piezoelectric elements are used to create the elliptical motions and are driven at near resonance frequencies to create the needed displacements for the motor to operate. The motor in this article consists of an arched frame, a center ground, and two piezoelectric elements connected to the center ground. Several finite element models were developed to design the motor and to predict performance. The models predicted a linear motor capable of pushing up to 5 N and a maximum speed of 0.4 m/s. A prototype frame was built out of tool steel and run against an oxide ceramic plate. The prototype motor achieved a maximum speed of 55.6 mm/s and a push force of 0.348 N at a preload of 6 N. The prototype frame’s steady-state displacements were approximately 20% of the expected output from the finite element models. Reasons for these discrepancies are discussed and investigated.

Extrinsic noise passing through a Michaelis–Menten reaction: A universal response of a genetic switch

The study of biochemical pathways usually focuses on a small section of a protein interactions network. Two distinct sources contribute to the noise in such a system: intrinsic noise, inherent in the studied reactions, and extrinsic noise generated in other parts of the network or in the environment. We study the effect of extrinsic noise entering the system through a nonlinear uptake reaction which acts as a nonlinear filter. Varying input noise intensity varies the mean of the noise after the passage through the filter, which changes the stability properties of the system. The steady-state displacement due to small noise is independent on the kinetics of the system but it only depends on the nonlinearity of the input function. For monotonically increasing and concave input functions such as the Michaelis–Menten uptake rate, we give a simple argument based on the small-noise expansion, which enables qualitative predictions of the steady-state displacement only by inspection of experimental data: when weak and rapid noise enters the system through a Michaelis–Menten reaction, then the graph of the system's steady states vs. the mean of the input signal always shifts to the right as noise intensity increases. We test the predictions on two models of lac operon, where TMG/lactose uptake is driven by a Michaelis–Menten enzymatic process. We show that as a consequence of the steady state displacement due to fluctuations in extracellular TMG/lactose concentration the lac switch responds in an asymmetric manner: as noise intensity increases, switching off lactose metabolism becomes easier and switching it on becomes more difficult.

Cavity quantum optomechanics of ultracold atoms in an optical lattice: Normal-mode splitting

We consider the dynamics of a movable mirror (cantilever) of a cavity coupled through radiation pressure to the light scattered from ultracold atoms in an optical lattice. Scattering from different atomic quantum states creates different quantum states of the scattered light, which can be distinguished by measurements of the displacement spectrum of the cantilever. We show that for large pump intensities the steady state displacement of the cantilever shows bistable behaviour. Due to atomic back-action, the displacement spectrum of the cantilever is modified and depends on the position of the condensate in the Brillouin zone. We further analyze the occurrence of splitting of the normal mode into three modes due to mixing of the mechanical motion with the fluctuations of the cavity field and the fluctuations of the condensate with finite atomic two-body interaction. The present system offers a novel scheme to coherently control ultracold atoms as well as cantilever dynamics.

A Simplified Dynamic Model for the Analysis of the Slider Off-Track Motion Due to Head-Disk Interactions

A five-degree-of-freedom model was developed for the analysis of the off-track motion of the magnetic head slider in a hard disk drive. The air bearing was integrated into the dynamic system by combining its stiffness and damping matrices with those of the suspension. Simulation was conducted for the slider in intermittent contact with circumferentially located bumps on a rotating magnetic disk. For a single bump, the excitation to the transverse displacement of the slider is close to that of an impulse. However, for multiple bumps in a sequence, the excitation gives an effect similar to that of a step force function. The maximum transverse displacement increases almost linearly with both the coefficient of friction and the skew angle. The average contact force is determined by the maximum contact force, the contact time ratio, and the shape factor of the contact force, which change with the bump spacing and the rotational speed of the disk. The steady-state transverse displacement is related to the average contact force. As the bump spacing decreases, the average contact force increases, resulting in a greater transverse displacement. Based on the system dynamic characteristics alone, changing the rotational speed of the disk has only a small impact on the average contact force and, thus, on the transverse displacement. At zero skew angle with the bump path close to a rear pad edge, significant transverse motion occurs because of the excited roll mode and the coupling between the roll angle and the transverse displacement. The off-track motion of the slider is dominated by the rotational mode of the actuator arm and the sway mode of the suspension, as verified by comparing the results of the transverse displacement from the 5DOF model to that from a 2DOF model of the transverse motions of the actuator arm and suspension. The effects of the roll angle on the transverse displacement through coupling were found to be responsible for the difference in the transverse displacements obtained from the two models.

Stability of the Steady-State Displacement of a Liquid Plug Driven by a Constant Pressure Difference along a Prewetted Capillary Tube

In this work we study the stability of a liquid plug driven along a capillary tube by a constant pressure difference. The methodology is based on the analysis of the values of the steady-state film thickness as a function of the plug length and the Capillary number, when the pressure drop and the Laplace number are fixed; thus, we extend our previous work where the plug was forced to move at a constant speed [Campana; et al. Stability of the steady-state motion of a liquid plug in a capillary tube. Ind. Eng. Chem. Res. 2007, 46, 1803]. The stability charts, built for selected values of the Laplace number and a wide range of the dimensionless parameters, show the existence of a small stable region whose size increases as the Laplace number is augmented.

Monitored steady-state excitation and recovery (MSSR) radiation force imaging using viscoelastic models

Acoustic radiation force imaging methods distinguish tissue structure and composition by monitoring tissue responses to applied radiation force excitations. Although these responses are a complex, multidimensional function of the geometric and viscoelastic nature of tissue, simplified discrete biomechanical models offer meaningful insight to the physical phenomena that govern induced tissue motion. Applying Voigt and standard linear viscoelastic tissue models, we present a new radiation force technique - monitored steady-state excitation and recovery (MSSER) imaging - that tracks both steady-state displacement during prolonged force application and transient response following force cessation to estimate tissue mechanical properties such as elasticity and viscosity. In concert with shear wave elasticity imaging (SWEI) estimates for Young's modulus, MSSER methods are useful for estimating tissue mechanical properties independent of the applied force magnitude. We test our methods in gelatin phantoms and excised pig muscle, with confirmation through mechanical property measurement. Our results measured 10.6 kPa, 14.7 kPa, and 17.1 kPa (gelatin) and 122.4 kPa (pig muscle) with less than 10% error. This work demonstrates the feasibility of MSSER imaging and merits further efforts to incorporate relevant mechanical tissue models into the development of novel radiation force imaging techniques.

Magnetorheological Bypass Damper Exploiting Flow Through a Porous Channel

A magnetorheological (MR) damper with a bypass valve containing porous media is developed. Movement of the piston forces MR fluid to flow from one side of the piston to the other, through an externally mounted bypass packed with magnetic spheres. The passageways between the spheres provide narrow, tortuous channels that act as a controllable valve when subjected to a magnetic field. A stationary magnetic coil is wrapped around the so-called porous valve, which is isolated from the MR fluid and external to the primary hydraulic cylinder. While flowing through the tortuous channels in the porous media created by the packed spheres, the MR fluid experiences varied local flow directions, and thus an external field can be applied in any direction to adjust damping levels. Additionally, the use of long channels, which are tightly packed to create narrow passageways, allows a very high damping force to be generated by a relatively compact damper. Furthermore, use of an externally mounted coil allows for maintenance accessibility, and the magnetic flux return path can be either empty (air) or any high permeability material. The damper is tested for steady-state sinusoidal displacements, and equivalent viscous damping and complex stiffness are computed. It is shown that the porous bypass valve MR damper can provide high controllable damping force and a wide force range.

Transient domain wall displacement under spin-polarized current pulses

This paper investigates the non steady-state displacement of magnetic domain walls in a nanostrip submitted to a time-dependent spin-polarized current flowing along the nanostrip. First, numerical micromagnetic simulations show that a domain wall can move under application of a current pulse, and that the displacement resulting from a conversion of the domain wall structure is quantized. The numerical findings are subsequently explained in the framework of simplified analytic models, namely the 1D model and the point-core vortex model. We then introduce the concept of an angle linked to the magnetization of a general domain wall, and show that it allows understanding the transient phenomena quite generally. Simple analytic formulas are derived and compared to experiments. For this, charts are given for the key parameters of the domain wall mechanics, as obtained from numerical micromagnetic simulations. We finally discuss the limitations of this work, by looking at the influence of temperature elevation under current, presence of a non-adiabatic term, and of disorder.

Phase analysis of actuator response for sub-optimal bang–bang and velocity cancellation control of base-isolated structures

Starting with simplified models of displacement response for a base-isolated structure supplemented with sub-optimal bang–bang control, we formulate models of phase analysis of actuator force direction in relation to system displacements and velocities. For the case of steady-state displacement response, we show that switching of the actuator force direction can neither be perfectly in phase with displacements, nor perfectly in phase with velocities. In practice, however, switching of the actuator force direction is ‘almost in phase’ with velocities and ‘almost orthogonal’ to sign changes in displacements. This observation suggests that a new and very simple velocity cancellation control might be effective in adding value to base isolation system responses. Numerical experiments are conducted to assess improvements in performance due to sub-optimal bang–bang control and velocity cancellation control, and to validate the extent to which the phase analysis predictions hold in linearly elastic and non-linear time-domain settings. Copyright © 2007 John Wiley & Sons, Ltd.

Tissue deformation induced by radiation force from Gaussian transducers

Imaging techniques based upon the tissue mechanical response to an acoustic radiation force are being actively researched. In this paper a model for predicting steady-state tissue displacement induced by a radiation force arising from the absorption of Gaussian ultrasound beams is presented. A simple analytic expression is derived that agrees closely with the numerical quadrature of the displacement convolution integrals. The analytic result reveals the dependence of the steady-state axial displacement upon the operational parameters, e.g., an inverse proportional relationship to the tissue shear modulus. The derivation requires that the transducer radius be small compared to the focal length, but accurate results were obtained for transducer radii comparable to the focal length. Favorable comparisons with displacement predictions for non-Gaussian transducers indicate that the theory is also useful for a broader range of transducer intensity profiles.

Piggyback tectonics: Long-term growth of Kilauea on the south flank of Mauna Loa

Compositional and age data from offshore pillow lavas and volcaniclastic sediments, along with on-land geologic, seismic, and deformation data, provide broad perspectives on the early growth of Kilauea Volcano and the long-term geometric evolution of its rift zones. Sulfur-rich glass rinds on pillow lavas and volcaniclastic sediments derived from them document early underwater growth of a large compositionally diverse alkalic edifice. The alkalic rocks yield 40Ar / 39Ar ages as old as about 275 ka; transitional-composition lavas, which mark beginning of the shield stage while most or all the edifice remained below sea level, probably first erupted after about 150 ka, and tholeiitic lavas of present-day type are probably younger than 100 ka. Breccia clasts from Papau Seamount and along the lower southwest corner of the Hilina bench are derived from subaerial Mauna Loa, requiring that Mauna Loa's flank underlies western parts of Kilauea at shallow depth. The volume of the Kilauea edifice is therefore smaller (∼10,000 km 3) than previous estimates (15–40,000 km 3); lava-thickness accumulation rates appear to have remained nearly constant during edifice growth, as effusion rates increased from ∼25 × 10 6 m 3/yr at end of the alkalic stage to the present-day tholeiite rate of ∼100 × 10 6 m 3/yr. Seismic and gravity data show that the deep plumbing system for Kilauea's magma supply extends nearly vertically through the oceanic crust at least to mantle depths of 30–35 km, directly below its present-day caldera. Proximity of Kilauea's caldera to the surface boundary with Mauna Loa and the presence of Mauna Loa rocks at shallow depth beneath the south flank are difficult to reconcile with a submarine origin for early Kilauea alkalic lavas, unless geometric relations between the two volcanoes have changed substantially during growth of the Kilauea shield. Seismic and ground deformation data suggest seaward spreading of the entire south flank of Hawaii Island, independently of the boundary between Kilauea and Mauna Loa, along a landward-dipping detachment fault system near the basal contact of the composite volcanic edifices with underlying oceanic crust. Current steady-state horizontal displacements increase seaward, at rates of ∼1.5 cm/yr on the lower flank of Mauna Loa and reaching 5–8 cm/yr at the Kilauea coastline. Infrequent (∼100 yr?) large earthquakes generate similar geometries, but 10 2 larger displacements per event. Present-day Kilauea is the more dynamic edifice, but prior to inception of Kilauea and during its early growth, Mauna Loa is inferred to have undergone intense volcano spreading, involving the Kaoiki–Honuapo fault system (considered a geometric analog of the Hilina system on Kilauea). Cumulative deformation of Mauna Loa's south flank during growth of Kilauea since 200–300 ka is estimated to have involved > 10 km of seaward spreading, displacing the rift zones of Kīlauea while its deep plumbing system and summit magma reservoir remained nearly fixed in space. Kilauea's rift zones, rather than migrating southward with time solely due to dike emplacement preferentially on the mobile seaward side, alternatively are interpreted to have been transported passively southward, “piggyback” style, during shield-stage growth of Kilauea as a blister on the still-mobile south flank of Mauna Loa. Such an evolution of Kilauea accounts for the arcuate geometry of the present-day rift zones, proximity of the summit magma supply to the exposed flank of Mauna Loa, initial submarine growth of the ancestral edifice, and present-day location of Mauna Loa rocks at shallow depth beneath the south flank of Kilauea.

The influence of polymer concentration and chain architecture on free surface displacement flows of polymeric fluids

We examine the effect of polymer concentration and chain architecture on the steady state displacement of polymeric fluids by air in between two infinitely long closely spaced parallel plates, i.e., Hele-Shaw flow. A stabilized finite element method coupled with a pseudosolid domain mapping technique is used for carrying out the computations. The constitutive equations employed in this study are the Finitely Extensible Nonlinear Elastic–Chilcott Rallison (FENE-CR) and the Finitely Extensible Nonlinear Elastic–Peterlin (FENE-P) models for dilute solutions, the Giesekus constitutive equation for dilute, semidilute and concentrated solutions, and the Extended Pom-Pom (XPP) constitutive equation for linear and branched polymeric melts. Our study indicates the presence of a recirculation flow at low Ca and a bypass flow at high Ca irrespective of polymer concentration and chain architecture. We show that the interfacial dynamics in both the recirculation and the by-pass flow depend on extensional hardening and shear thinning characteristics of the fluids. In the recirculation flow, we observe the formation of normal elastic stress boundary layers in the capillary transition region, an accompanying increase in the film thickness and a compression of the bubble in the capillary transition region, at moderate Wi. In the bypass flow, in addition to the elastic stress boundary layer in the capillary transition region, an additional stress boundary layer is observed at the tip of the bubble. The amount of film thickening, the magnitude of the stress in the stress boundary layer and the amount of bubble compression are largest for the most extensional hardening fluids and reduce with decreasing extensional hardening and increasing shear thinning. We show that the film thickness is determined by two competing forces, i.e., normal stress gradients in the flow direction, in the capillary transition region (recirculation flow) and the tip region (bypass flow) and shear stress gradientsin the gap direction. For both the recirculation and the bypass flow, we show how the film thickness scales with fluid normal stresses and shear viscosities, and develop correlations for the film thickness as a function of Ca and Wi.